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Necessary and sufficient conditions for asymptotic decay of oscillations in delayed functional equations†
Published online by Cambridge University Press: 14 November 2011
Synopsis
This paper studies the equation
where the differential operator Ln is defined by
and a necessary and sufficient condition that all oscillatory solutions of the above equation converge to zero asymptotically is presented. The results obtained extend and improve previous ones of Kusano and Onose, and Singh, even in the usual case where
where N is an integer with l≦N≦n–1.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 91 , Issue 1-2 , 1981 , pp. 135 - 145
- Copyright
- Copyright © Royal Society of Edinburgh 1981